Many assays and related tests quantify a physical property of a sample by comparing a measured assay value against an assay curve for the physical property of interest. For example, a blood sample may contain some initially unknown level of a particular pathogen. When the sample is evaluated with an assay for the pathogen of interest, it provides a measurable signal that tends to be monotonically changing according to (and typically somewhat proportional to, at least in a log—log representation) the pathogen level in the patient's blood.
Examples of measured signals include luminescence or radiation emitted from a test sample, PCR-based methods, the absorption coefficient of the sample, the color of a sample, etc. These different ways or platforms for measuring the same quantity are not easily usable together as they do not quantify to the same scale. For comparing and combining phenomenological information and observations, researchers have needs for easily converting measurements taken by one platform to the scale used by another platform. For example, a researched may need to integrate data comprising measurements taken on a luminescence platform with those taken on a radiation platform. Even measurements taken with similar platforms, such as a single channel microarray versus a dual channel microarray need to be converted in order to be usable together. Thus there is a need for improved methods and tools for normalizing data from different platforms so that they are based upon the same scale.
In a typical case, the assay procedure involves contacting a test sample (analyte) with a test solution followed by a washing step. Thereafter, the test quantity of interest is measured and compared against an assay curve (sometimes referred to as a “response curve”). The assay curve provides the measured value as a dependent variable and the “true value” (that is unknown, but approximate) of the property of interest as an independent variable. In one specific example, an assayed sample of hepatitis B virus (HBV) DNA emits light of a luminescence that varies with viral load. Thus, the luminescence of the sample is detected and compared against the assay curve that specifies a corresponding value of viral load for the sample.
In most useful assays, the assay curve increases monotonically with the property of interest over the dynamic range (e.g., luminescence increases monotonically with viral load). Often the assay is designed so that the response of the assay is nearly linear over a specific dynamic range. To achieve this, the assay curve may be expressed as the logarithm of the measured value versus the logarithm of the property value. In practice, however, such assay curves rarely assume a truly linear form. Frequently, there is a slight curvature over the dynamic range which can be better represented by a quadratic expression. Further, near or just beyond the limits of the specific dynamic range, the response curve often flattens (i.e., the measured value changes only slightly with respect to changes in the true property value) to give the overall response curve, essentially a “sigmoid” shape.
Even with widely used and validated assays, one is never certain that the specified property value for a sample is truly accurate. For example, the calibration of an assay may be inaccurate because the “standard” used to generate the assay curve is itself inaccurate. Sometimes, the property value of a standard changes slightly with time. And sometimes when a standard runs out, the new standard created to replace the old does not possess the same true property value as the old standard. Further, while a given assay may be internally consistent over a period of time, it is still very difficult or impossible to accurately correlate two different assays for the same analyte.
Many applications could benefit from improved confidence in measurements of the property value consistent across assays. For example, one might want to use two or more different assays to monitor the same property value. A hepatitis B patient may have had his viral load monitored with a first assay that becomes temporarily unavailable. When a second assay—which relies on an entirely different physical mechanism than the first assay—is used in place of the first and gives a rather high reading of viral load, it could mean either (a) the patient's viral load is truly increasing or (b) the second assay employs an assay curve that, in comparison to the first assay's curve, gives a higher property value reading for a given sample. Obviously, an attending health care professional needs a reliable value consistent with both assays.
Also, parametric models for predicting the outcome of a medical treatment or other course of action are created from prognostic variables relevant to the models (e.g., assay results). The accuracy of the model is improved as more-consistent data is used to construct it. If that data is provided as assay results for two or more assays, there must be some way to establish a conversion between the assay results of the two or more assays. Otherwise the resulting model may fail to accurately handle inputs from one or more of the assays used to construct the model.
Other applications exist that require a conversion between property values specified by multiple assays or methods. For example, when an enterprise generates a new assay standard it must accurately correlate that standard's property value to the old standard's property value. Otherwise, assays using the new standard will not be consistent with the same assays using the old standard.
In another example, enterprises may need to compare two assays' performance (e.g., sensitivity and responsiveness) when those assays are designed to quantitate the same analyte. Several commercial assays are available for HBV DNA quantification, and laboratory managers need tools to assess how well the various assays operate. Even when results are reported in the same unit of quantification for a given sample, different assays report different results. Thus, the person conducting the comparison must ensure that the response curves of the two assays can be plotted on the same independent variable axis (the true property value axis).
Traditionally, when comparing multiple assays or batches of a standard, one uses a regression analysis to quantify the associations of interest. For example, for a series of samples, the measured values of a first assay or batch is provided as the independent variable and the measured values of the second assay or batch is provided as the dependent variable. Then one assumes a relationship between the independent and dependent variables (e.g., a linear or quadratic relationship) and a regression analysis is performed to identify parameters of the relationship that nicely fit the data. Unfortunately, linear regression analysis is restricted to comparison of only two assays at a time. Still further, this application of regression tends to violate a primary assumption for correct inference of results, i.e., the independent variable is assumed to be more precise versus the dependent variable. See e.g., Yonathan Bard, “Nonlinear Parametric Estimation,” Academic Press, New York, N.Y., 1974. Hence, the more precise variable must be the independent regression variable, typically denoted as x, while the noisier variable must be the dependent or response variable, denoted y. In many assay comparisons, where one assay is selected to be y variable and the other x variable, the results are questionable since the assay errors are comparable or, worse, the x variable error is larger than the y variable error.
Hence, there is a need to compare multiple assays (or other methods) or batches of standard without the inherent bias of linear regression, to be able to convert values between the different assays or standards, and to provide a property basis consistent across all assays.